NUMBER STRINGS
WHY USE NUMBER STRINGS:
Number Strings are a set of number related clues that solve a computation
problem. Students listen to the clues and arrive at a solution. Then the student
shares the answer and justifies how he/she arrived at that answer. In a number
string, there can be any of number clues. We would suggest beginning with 2 clues
and working up to 5 for primary students and staying with addition and subtraction
operations until the students have had some experience with halving and doubling
numbers and making easy fair shares.
Using Number String problems is a way to help students develop not only mental
computation skills, but also their listening and speaking skills. The added challenge
of using numbers used in the real world, helps the student develop the ability to
apply real world numbers in their computations. As students share their thinking,
they are developing their quantitative and abstract reasoning and communication
skills. Sharing and listening to peers helps students evaluate another person's
justifications. Writing and creating their own number string problems is offering a
very important critical thinking opportunity - well worth the time taken to develop
these kinds of problems throughout the school year.
HOW TO MAKE NUMBER STRINGS CARDS:
1. The easiest way is to copy the cards on cardstock and cut them out. You
can keep them together using a binder ring, and flip to a new card as part of
your mental math/number talk time.
2. You can print the cards off on label paper. (We used the Avery 5160
template, which is for larger address labels). You can then stick the labels
to index cards, or on cardstock. If you keep the answers on the cards, you
can fold over an end to cover them, or use a post it note to hide the
answers.
HOW TO USE NUMBER STRINGS:
1. The Common Core State Standards advocates for developing strategies
for solving computational problems mentally. During a "Number Talk" or a
"Convince Me" conversation, slowly share one clue at a time. The students
mentally calculate each clue and use the stated operation to find the answer.
The clues continue until all the clues on one card have been shared. Students
then share their reasoning and justify the solution. These kinds of problems
can be sprinkled occasionally in daily number talks - offering a variety of
computational opportunities, and several opportunities to differentiate in the
classroom.
2. A number string can also be displayed in the classroom at the beginning of the
week. Sometime during the week, the students are asked to find the solution
and write about their thinking in their math journals. In this way, the teacher can
assess whether the students are able to apply the clues correctly.
3. Another way to use a set of number strings over and over again is to pass out a
number string clue set to each pair of students in your class. Together they
work to solve the clues and arrive at a solution they can defend. Then each pair
of students is paired with another pair of students to discuss their reasoning for
their set of clues. On another day, pass out the clues again. Most of them will
get a different set of clues to explore. If a pair of students would get the very
same clue set as before, they can solve the number string again. Perhaps they
work faster or think of a more effective reasoning strategy this time around.
4. Once students get very familiar with solving number strings, the teacher can
assign the students to write their own number string problems. When students
are ready for this challenge, brainstorm important numbers used in
measurements such the number of inches in a foot, or numbers used in telling
time, number amounts in our monetary system, extended place values, and so
on. This list of ways numbers are used in the real world is a necessary scaffold
for building meaningful and challenging number strings. This is also a great
activity for older students to partner with younger students.
5. Teachers can begin number string problems at a very early age. In
Kindergarten, 2+ 2 + 1 can be a form of a number string problem when the
students are working on adding fluently (addition and subtraction problems to
5).
6. Have fun with these kinds of problems. Challenging our students and working
on mental math is a great way to engage students in mathematical thinking!
For more number strings, follow our TpT store.
We plan to post new lessons and monthly number strings
that you can add to your collection!
http://www.teacherspayteachers.com/Store/Teaching-Learning-Collaborative
Also, when you get a chance, be sure to rate our Number Strings activity!
Thanks for downloading!
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can
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Number strings cards
to use with students
2.
1.
Start
with
the
number
of
halves
in
a
whole.
Triple
it.
Add
the
number
of
sides
on
a
triangle.
Subtract
the
number
of
sides
on
a
rectangle.
Add
the
number
of
days
in
a
week.
Begin
with
the
number
of
hours
in
a
day.
Subtract
4.
Subtract
half
of
that
number.
Add
the
number
of
legs
on
an
octopus.
Subtract
a
dozen.
Double
that
number.
Add
the
number
of
inches
in
a
foot
4.
3.
Take
the
number
of
sides
on
a
rectangle.
Begin
with
the
number
of
continents
on
Earth.
Add
the
number
of
sides
on
a
square.
Add
the
number
of
oceans
on
Earth.
Add
the
number
of
faces
on
a
pyramid.
Add
that
number
to
the
number
of
sides
on
a
triangle.
Add
the
number
of
inches
in
a
yard.
Subtract
the
number
of
vertices
on
a
square.
Subtract
the
number
of
Cardinal
Directions
on
a
Compass
Rose.
5.
Begin
with
the
number
of
legs
on
an
ant.
6.
Begin
with
the
number
of
days
in
a
year.
Multiply
by
the
number
of
legs
on
a
spider.
Subtract
the
number
of
months
in
a
year.
Divide
that
number
in
half.
Subtract
the
number
of
days
in
January.
Subtract
by
the
number
of
legs
on
a
dog.
Add
the
number
of
days
in
a
week.
Add
the
number
of
minutes
in
an
hour.
8.
7.
Start
with
the
number
of
sides
on
a
trapezoid.
Begin
with
two
dozen
eggs.
Triple
that
number.
Add
to
that
the
number
for
the
day
of
the
month
that
we
celebrate
Independence
Day.
Add
the
number
of
sides
on
a
pentagon.
Divide
that
number
in
half.
Add
the
number
of
vertices
on
a
pentagon.
Subtract
that
number
from
itself.
Add
the
number
of
sides
on
an
octagon.
9.
10.
Start
with
half
of
ten.
Start
with
the
number
of
pennies
in
five
dimes.
Multiply
that
by
10.
Subtract
the
number
of
pennies
in
3
nickels.
Subtract
15
minutes.
Double
that
number.
Add
that
number
three
times.
Add
the
number
of
pennies
in
4
quarters.
Add
the
pennies
in
a
dollar
bill.
Subtract
the
number
of
pennies
in
2
dimes.
11.
12.
Start
with
the
missing
addend
in
3
+
?
=
11.
Start
with
the
number
of
sides
on
a
quadrilateral.
Add
10
more.
Add
the
number
of
sides
on
an
octagon.
Subtract
2.
Add
the
number
of
faces
on
a
cube.
Add
the
number
of
quarter
circles
in
a
whole
circle.
Add
the
number
of
vertices
on
a
cone.
Subtract
the
number
of
sides
on
a
parallelogram.
Add
the
number
of
sides
in
two
hexagons.
13.
14.
Start
with
the
number
that
is
more
…
26
or
36?
Start
with
the
even
number
…
436
or
437.
Add
the
number
of
minutes
in
a
half
hour.
Subtract
100
four
times.
Subtract
the
number
equal
to
16
+
16.
What
is
100
more?
Add
six
tens.
Count
back
1.
Subtract
the
number
of
pennies
in
a
quarter.
Count
back
by
fives
three
times.
15
16.
Start
with
the
even
number
…
22
or
27.
Add
the
number
of
inches
in
a
foot.
Subtract
the
30
centimeters.
Add
the
number
of
feet
in
a
yard.
Add
the
number
of
inches
in
a
yard.
Start
with
the
odd
number
…
41
or
48.
Add
2
tens
and
3
ones.
Subtract
2
tens
and
4
ones.
Double
that
number.
Double
7
and
add
it
to
your
number.
17.
18.
Start
with
1
hundred
2
tens
and
5
ones.
Start
with
the
difference
between
15
–
9.
Subtract
3
tens.
Add
the
number
of
sides
on
4
triangles.
Subtract
1
ten
and
9
ones.
Add
6
+
7.
Add
5
tens
and
5
ones.
Add
the
number
of
sides
on
2
hexagons.
Subtract
the
number
of
sides
on
2
octagons.
Add
the
number
of
angles
in
a
rectangle.
19.
20.
Start
with
the
number
of
yards
on
a
football
field.
Start
with
11
and
double
it.
Add
the
number
of
football
players
on
the
field
Add
the
sum
for
8
+
5.
for
just
your
team.
Subtract
the
2.
Add
the
number
of
points
for
3
touchdowns.
Double
that.
Subtract
the
number
of
points
for
2
field
goals.
Subtract
6
tens.
Add
the
100
kernels
of
corn
you
ate
during
half
time.
21.
22.
Start
with
the
number
of
players
on
a
basketball
court.
Start
with
the
number
of
bases
in
3
cylinders.
Add
the
number
of
angles
in
a
trapezoid.
Add
the
number
of
points
for
11
regular
baskets.
Subtract
1
free
throw.
Subtract
4
for
the
number
of
players
who
fouled
out!
Add
the
number
of
sides
in
4
rhombi.
Add
the
number
of
angles
in
a
decagon.
Subtract
6
rows
of
5.
23.
24.
Use
the
“Make
a
Ten”
strategy
to
find
the
sum:
7
+
8
=
10
+
?
Then
start
with
the
missing
number
–(?).
Start
with
the
number
of
feet
on
four
ducks.
Each
duck
eats
2
fish.
Add
that
number.
Add
4
rows
of
6.
Add
3
rows
of
5.
Subtract
2
rows
of
10.
Add
10
rows
of
10.
Add
61
ducks
who
flew
into
the
pond.
Subtract
the
15
pieces
of
bread
found
on
the
ground.
Add
3
ducks
who
joined
the
other
ducks
in
the
pond.
25.
26.
Start
with
the
number
of
minutes
in
an
hour.
Start
with
the
number
that
is
2
less
than
107.
Add
the
number
of
hours
in
a
day.
Add
5
rows
of
5.
Subtract
the
number
of
minutes
in
a
half
hour.
Add
the
number
that
is
2
more
than
48.
Add
the
number
of
minutes
in
a
quarter
of
an
hour.
Subtract
100.
Subtract
the
number
of
seconds
in
a
minute.
Add
half
of
30.
27.
28.
There
are
4
whole
and
equal
circles,
begin
with
half
of
them.
Start
with
the
number
of
pennies
in
one
dime.
Add
the
number
of
pennies
in
7
dimes.
Add
the
number
of
halves
in
one
whole
circle.
Add
1
more
than
57
circles.
Subtract
half
of
that
number.
Add
the
number
of
pennies
in
8
nickels.
Subtract
the
number
of
pennies
in
1
dollar.
Add
the
pennies
in
two
quarters
and
1
nickel.
Add
2
less
than
8.
29.
30.
Start
with
a
dozen.
Start
with
the
number
10
more
than
30.
Double
that
dozen.
Add
four
rows
of
ten
cars.
Subtract
half
of
16.
Add
the
number
of
wheels
on
a
2
cars.
Add
the
number
days
in
a
week.
Subtract
the
number
of
wheels
on
a
tricycle.
Add
25
pennies.
Add
the
number
of
wheels
on
a
regular
bike.
Number strings cards
with answers
2.
1.
Start
with
the
number
of
halves
in
a
whole.
2
Begin
with
the
number
of
hours
in
a
day.
24
Triple
it.
6
Subtract
4.
9
Subtract
half
of
that
number.
Add
the
number
of
sides
on
a
triangle.
Subtract
the
number
of
sides
on
a
rectangle.
5
Add
the
number
of
days
in
a
week.
12
20
10
Add
the
number
of
legs
on
an
octopus.
18
Subtract
a
dozen.
6
Double
that
number.
12
Add
the
number
of
inches
in
a
foot
24
4.
3.
Take
the
number
of
sides
on
a
rectangle.
4
Begin
with
the
number
of
continents
on
Earth.
7
Add
the
number
of
sides
on
a
square.
8
Add
the
number
of
oceans
on
Earth.
12
Add
the
number
of
faces
on
a
pyramid.
17
Add
that
number
to
the
number
of
sides
on
11
a
triangle.
Add
the
number
of
inches
in
a
yard.
Subtract
the
number
of
vertices
on
a
square.
Subtract
the
number
of
Cardinal
Directions
13
on
a
Compass
Rose.
47
43
5.
Begin
with
the
number
of
legs
on
an
ant.
6.
6
Begin
with
the
number
of
days
in
a
year.
365
Multiply
by
the
number
of
legs
on
a
spider.
48
Subtract
the
number
of
months
in
a
year.
353
Divide
that
number
in
half.
24
Subtract
the
number
of
days
in
January.
322
Subtract
by
the
number
of
legs
on
a
dog.
20
Add
the
number
of
days
in
a
week.
329
Add
the
number
of
minutes
in
an
hour.
389
8.
7.
Start
with
the
number
of
sides
on
a
trapezoid.
4
Begin
with
two
dozen
eggs.
24
Triple
that
number.
12
Add
to
that
the
number
for
the
day
of
the
month
28
that
we
celebrate
Independence
Day.
Add
the
number
of
sides
on
a
pentagon.
17
Divide
that
number
in
half.
14
Add
the
number
of
vertices
on
a
pentagon.
22
Subtract
that
number
from
itself.
0
Add
the
number
of
sides
on
an
octagon.
30
9.
10.
Start
with
half
of
ten.
5
Start
with
the
number
of
pennies
in
five
dimes.
50
Multiply
that
by
10.
50
Subtract
the
number
of
pennies
in
3
nickels.
35
Subtract
15
minutes.
35
Add
the
number
of
pennies
in
4
quarters.
135
Double
that
number.
70
Add
that
number
three
times.
210
Add
the
pennies
in
a
dollar
bill.
235
Subtract
the
number
of
pennies
in
2
dimes.
215
11.
12.
Start
with
the
missing
addend
in
3
+
?
=
11.
8
Start
with
the
number
of
sides
on
a
quadrilateral.
4
Add
10
more.
18
Add
the
number
of
sides
on
an
octagon.
12
Subtract
2.
16
Add
the
number
of
faces
on
a
cube.
18
Add
the
number
of
quarter
circles
in
a
whole
20
circle.
Add
the
number
of
vertices
on
a
cone.
19
Subtract
the
number
of
sides
on
a
parallelogram.
15
Add
the
number
of
sides
in
two
hexagons.
32
13.
14.
Start
with
the
number
that
is
more
…
26
or
36?
36
Start
with
the
even
number
…
436
or
437.
436
Add
the
number
of
minutes
in
a
half
hour.
66
Subtract
100
four
times.
36
Subtract
the
number
equal
to
16
+
16.
34
What
is
100
more?
134
Add
six
tens.
96
Count
back
1.
95
Subtract
the
number
of
pennies
in
a
quarter.
109
Count
back
by
fives
three
times.
15.
16.
Start
with
the
even
number
…
22
or
27.
22
Add
the
number
of
inches
in
a
foot.
34
Subtract
the
30
centimeters.
4
Add
the
number
of
feet
in
a
yard.
7
Add
the
number
of
inches
in
a
yard.
43
80
Start
with
the
odd
number
…
41
or
48.
41
Add
2
tens
and
3
ones.
64
Subtract
2
tens
and
4
ones.
40
Double
that
number.
80
Double
7
and
add
it
to
your
number.
94
17.
18.
Start
with
1
hundred
2
tens
and
5
ones.
125
Start
with
the
difference
between
15
–
9.
6
Subtract
3
tens.
Add
the
number
of
sides
on
4
triangles.
18
95
150
Subtract
1
ten
and
9
ones.
131
Add
6
+
7.
144
Add
5
tens
and
5
ones.
Add
the
number
of
sides
on
2
hexagons.
30
Subtract
the
number
of
sides
on
2
octagons.
14
Add
the
number
of
angles
in
a
rectangle.
18
19.
20.
Start
with
the
number
of
yards
on
a
football
field.
100
Start
with
11
and
double
it.
22
Add
the
number
of
football
players
on
the
field
111
Add
the
sum
for
8
+
5.
35
for
just
your
team.
Subtract
the
2.
33
Add
the
number
of
points
for
3
touchdowns.
129
Double
that.
66
Subtract
the
number
of
points
for
2
field
goals.
123
Subtract
6
tens.
6
Add
the
100
kernels
of
corn
you
ate
during
223
half
time.
21.
22.
Start
with
the
number
of
players
on
a
basketball
5
court.
Start
with
the
number
of
bases
in
3
cylinders.
6
Add
the
number
of
angles
in
a
trapezoid.
10
Add
the
number
of
points
for
11
regular
baskets.
27
Subtract
1
free
throw.
26
Subtract
4
for
the
number
of
players
who
fouled
22
out!
Add
the
number
of
sides
in
4
rhombi.
26
Add
the
number
of
angles
in
a
decagon.
36
Subtract
6
rows
of
5.
6
23.
24.
Use
the
“Make
a
Ten”
strategy
to
find
the
sum:
5
7
+
8
=
10
+
?
Then
start
with
the
missing
number
–(?).
Start
with
the
number
of
feet
on
four
ducks.
8
Each
duck
eats
2
fish.
Add
that
number.
24
Add
4
rows
of
6.
29
Add
3
rows
of
5.
44
Subtract
2
rows
of
10.
24
Add
10
rows
of
10.
124
Add
61
ducks
who
flew
into
the
pond.
85
Subtract
the
15
pieces
of
bread
found
on
70
the
ground.
Add
3
ducks
who
joined
the
other
ducks
73
in
the
pond.
25.
26.
Start
with
the
number
of
minutes
in
an
hour.
60
Start
with
the
number
that
is
2
less
than
107.
105
Add
the
number
of
hours
in
a
day.
84
Add
5
rows
of
5.
130
Subtract
the
number
of
minutes
in
a
half
hour.
54
Add
the
number
that
is
2
more
than
48.
180
Add
the
number
of
minutes
in
a
quarter
of
an
hour.
69
Subtract
100.
80
Subtract
the
number
of
seconds
in
a
minute.
9
Add
half
of
30.
95
27.
28.
There
are
4
whole
and
equal
circles,
begin
with
2
half
of
them.
Start
with
the
number
of
pennies
in
one
dime.
10
Add
the
number
of
pennies
in
7
dimes.
80
Add
the
number
of
halves
in
one
whole
circle.
4
Add
1
more
than
57
circles.
62
Subtract
half
of
that
number.
31
Add
the
number
of
pennies
in
8
nickels.
120
Subtract
the
number
of
pennies
in
1
dollar.
20
Add
the
pennies
in
two
quarters
and
1
nickel.
75
Add
2
less
than
8.
37
29.
30.
Start
with
a
dozen.
12
Start
with
the
number
10
more
than
30.
40
Double
that
dozen.
24
Add
four
rows
of
ten
cars.
Subtract
half
of
16.
16
Add
the
number
of
wheels
on
a
2
cars.
88
Add
the
number
days
in
a
week.
23
80
Subtract
the
number
of
wheels
on
a
tricycle.
85
Add
25
pennies.
48
Add
the
number
of
wheels
on
a
regular
bike.
87
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